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Entrance path category of a stratified space

Mathematical Conversations

Topic:

Entrance path category of a stratified space

Speaker:

Amit Patel

Affiliation:

Member, School of Mathematics

Date:

Wednesday, April 6

Time/Room:

6:00pm - 7:00pm/Dilworth Room

A covering space $C \to M$ is classified by a subgroup of the fundamental group of $M$. If we refuse to choose a basepoint, then $C \to M$ is equivalent to a functor from the fundamental groupoid of $M$ to $\mathsf{Set}$. Suppose $(M,S)$ is a stratified space and $(C, T) \to (M,S)$ a stratified covering. Then $(C, T) \to (M,S)$ is equivalent to a functor from the entrance path category $\mathsf{Ent}(M,S)$ of $(M,S)$ to $\mathsf{Set}$. In general, any $S$-constructible cosheaf over $M$ is equivalent to a functor from $\mathsf{Ent}(M,S)$. I will introduce the entrance path category and argue this equivalence.